.TH  SLAED6 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " 
.SH NAME
SLAED6 - the positive or negative root (closest to the origin) of  z(1) z(2) z(3) f(x) = rho + --------- + ---------- + ---------  d(1)-x d(2)-x d(3)-x  It is assumed that   if ORGATI = .true
.SH SYNOPSIS
.TP 19
SUBROUTINE SLAED6(
KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )
.TP 19
.ti +4
LOGICAL
ORGATI
.TP 19
.ti +4
INTEGER
INFO, KNITER
.TP 19
.ti +4
REAL
FINIT, RHO, TAU
.TP 19
.ti +4
REAL
D( 3 ), Z( 3 )
.SH PURPOSE
SLAED6 computes the positive or negative root (closest to the origin)
of
                 z(1)        z(2)        z(3)
f(x) =   rho + --------- + ---------- + ---------
                d(1)-x      d(2)-x      d(3)-x
      otherwise it is between d(1) and d(2)
.br

This routine will be called by SLAED4 when necessary. In most cases,
the root sought is the smallest in magnitude, though it might not be
in some extremely rare situations.
.br

.SH ARGUMENTS
.TP 13
KNITER       (input) INTEGER
Refer to SLAED4 for its significance.
.TP 13
ORGATI       (input) LOGICAL
If ORGATI is true, the needed root is between d(2) and
d(3); otherwise it is between d(1) and d(2).  See
SLAED4 for further details.
.TP 13
RHO          (input) REAL            
Refer to the equation f(x) above.
.TP 13
D            (input) REAL array, dimension (3)
D satisfies d(1) < d(2) < d(3).
.TP 13
Z            (input) REAL array, dimension (3)
Each of the elements in z must be positive.
.TP 13
FINIT        (input) REAL            
The value of f at 0. It is more accurate than the one
evaluated inside this routine (if someone wants to do
so).
.TP 13
TAU          (output) REAL            
The root of the equation f(x).
.TP 13
INFO         (output) INTEGER
= 0: successful exit
.br
> 0: if INFO = 1, failure to converge
.SH FURTHER DETAILS
30/06/99: Based on contributions by
.br
   Ren-Cang Li, Computer Science Division, University of California
   at Berkeley, USA
.br

10/02/03: This version has a few statements commented out for thread safety
   (machine parameters are computed on each entry). SJH.
.br

05/10/06: Modified from a new version of Ren-Cang Li, use
   Gragg-Thornton-Warner cubic convergent scheme for better stability.

